Rank-weight spec: TDNN exact (Demirkaya two-scale DNN, k = 1)

Returns a rank_weight spec whose eval_batch uses the exact TDNN rank table from tdnn_rank_table_exact(). The rank table is computed once per sample size n and cached inside the spec closure, so calling rank_weight_eval_batch() repeatedly on rank matrices of the same size does not recompute the table.

Usage

rank_weight_tdnn_exact(s1, s2, dim)

Arguments

s1

Positive integer; smaller U-statistic order (s1 < s2).

s2

Positive integer; larger U-statistic order.

dim

Positive integer; localization dimension. For standard Euclidean ranking this is ncol(X); for custom distances it should be set explicitly.

Value

A rank_weight spec (list with class "rank_weight").

Details

Signed weights. TDNN weights are a signed linear combination of two DNN tables and can be negative. They sum to 1 across all n observations but the negative entries are part of the bias-correction mechanism and should not be interpreted as a standard probability mass.

See also

rank_weight_tdnn_asymp(), tdnn_rank_table_exact(), weights_tdnn_exact()

Examples

rw <- rank_weight_tdnn_exact(s1 = 3L, s2 = 6L, dim = 2L)
R <- matrix(c(2L, 1L, 3L, 4L, 5L, 6L,
              6L, 2L, 1L, 3L, 4L, 5L), nrow = 6)
W <- rank_weight_eval_batch(rw, R)
colSums(W)  # c(1, 1)
#> [1] 1 1